The given sentence is in the active voice, as the subject 'Nobody' performs an action 'told' against the object 'me'.
If this sentence is changed to passive voice, then the object takes the place of the subject and vice versa and the word
'by' is introduced as now the subject receives the action by the object.
The verb form of the sentence is also changed from active form to
passive.
'Subject (Nobody) + verb (told) + object (me) + relative clause (that George was ill)' changes to:
'New subject (I) + verb (wasn't told) + relative clause (that George was ill) + by + new object (anybody)'
The pronouns nobody, somebody, anybody, they, when placed in passive voice, can be eliminated. Because they are indefinite pronouns and do not refer to a specific person, they can be merely implied in the passive voice. Hence the word 'nobody' can be removed.
Also, 'nobody' is a negative word (not anybody) and in the passive voice, the verb can be changed to negative 'wasn't told' instead.
This can be seen in option B, hence it's the right answer.
Option
A: The verb form 'ain't' is informal and is not used in the preferred formal English here. Also, 'ain't' which is a contraction of 'am not' is in present tense whereas the given sentence is in past tense 'told'.
Option C: The voice in the given sentence has not been changed to passive: 'Nobody told me' is still in active voice.
Option D: ''Haven't been told' is in the present perfect tense whereas the verb here is in the simple past tense 'told'.
Hence options A, C and D are incorrect.